Rank gain of Jacobians over number field extensions with prescribed Galois groups
Rank gain of Jacobians over number field extensions with prescribed Galois groups
Abstract We investigate the rank gain of elliptic curves, and more generally, Jacobian varieties, over nonâGalois extensions whose Galois closure has a Galois group permutationâisomorphic to a prescribed group G (in short, â G âextensionsâ). In particular, for alternating groups and (an infinite family of) projective linear groups G , âŚ